(x+2)(x-2)=3x+2 eching

$$( x + 2 ) ( x - 2 ) = 3 x + 2$$

x uchun yechish

$$x = \frac{\sqrt{33} + 3}{2} \approx 4,372281323$$

$$x=\frac{3-\sqrt{33}}{2}\approx -1,372281323$$

Kvadrat tenglamalaridan foydalanish qoidalari

Hisoblang: \left(x+2\right)\left(x-2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

$$x^{2}-4=3x+2$$

Ikkala tarafdan 3x ni ayirish.

$$x^{2}-4-3x=2$$

Ikkala tarafdan 2 ni ayirish.

$$x^{2}-4-3x-2=0$$

-6 olish uchun -4 dan 2 ni ayirish.

$$x^{2}-6-3x=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-3x-6=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va -6 ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-6\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-6\right)}}{2}$$

-4 ni -6 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+24}}{2}$$

9 ni 24 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{33}}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{33}}{2}$$

x=\frac{3±\sqrt{33}}{2} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{33} ga qo'shish.

$$x=\frac{\sqrt{33}+3}{2}$$

x=\frac{3±\sqrt{33}}{2} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{33} ni ayirish.

$$x=\frac{3-\sqrt{33}}{2}$$

Tenglama yechildi.

$$x=\frac{\sqrt{33}+3}{2} x=\frac{3-\sqrt{33}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

Hisoblang: \left(x+2\right)\left(x-2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 2 kvadratini chiqarish.

$$x^{2}-4=3x+2$$

Ikkala tarafdan 3x ni ayirish.

$$x^{2}-4-3x=2$$

4 ni ikki tarafga qo’shing.

$$x^{2}-3x=2+4$$

6 olish uchun 2 va 4'ni qo'shing.

$$x^{2}-3x=6$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=6+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=6+\frac{9}{4}$$

6 ni \frac{9}{4} ga qo'shish.

$$x^{2}-3x+\frac{9}{4}=\frac{33}{4}$$

x^{2}-3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{33}{4}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{33}{4}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{\sqrt{33}}{2} x-\frac{3}{2}=-\frac{\sqrt{33}}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{\sqrt{33}+3}{2} x=\frac{3-\sqrt{33}}{2}$$